I know a couple higher level athletes that are using peptide injections to treat various injuries... tendonitis, ligament, muscle etc... There are references to peptides that are on the WADA list and not allowed, but it appears there are others that are allowed and only used in the case of injury. They swear by em.

What do you know about them and is it true that the harmful side effects are minimal to none. From what I've read about the various peptides it appears to be a miraculous cure type scenario if the correct peptide is used.

Has the FDA considered approving for human consumption / use as treatment for anything that you know of?

Below is the abstracted summaries of relevant articles in humans using peptide and dipeptide supplements. Please note that all humans consume peptides and dipeptides every day as these are basically amino acids, the basic building blocks of proteins. There are some hormones that are composed of peptides including WADA banned anabolic steroids. Any time any supplement is taken, the supplement user runs the risk of getting supplements that are deliberately tainted by the manufacturers with anabolic steroids or their precursors without listing these ingredients to get better results for their muscle building product. Caveat emptor, the principle that the buyer is responsible for checking the quality and suitability of goods before a purchase is made, must be adhered to with all supplements. Pro-racers have been banned due to taking tainted supplements. So review the summaries I have included below. The data shows some positive effects on biochemical markers, but no data shows improving performance or speeding recovery significantly. All the studies were small. My recommendations, do not jump on the peptide, dipeptide supplement wagon at this point in time. More research needs to be done and WADA may decide that these are performance enhancing supplements that warrant banning.

Int J Sport Nutr Exerc Metab. 2015 Dec;25(6):541-9. doi: 10.1123/ijsnem.2015-0046. Epub 2015 May 22.
β-Alanine Supplementation Does Not Augment the Skeletal Muscle Adaptive Response to 6 Weeks of Sprint Interval Training.
Cochran AJ1, Percival ME, Thompson S, Gillen JB, MacInnis MJ, Potter MA, Tarnopolsky MA, Gibala MJ.
Author information
Abstract
Sprint interval training (SIT), repeated bouts of high-intensity exercise, improves skeletal muscle oxidative capacity and exercise performance. β-alanine (β-ALA) supplementation has been shown to enhance exercise performance, which led us to hypothesize that chronic β-ALA supplementation would augment work capacity during SIT and augment training-induced adaptations in skeletal muscle and performance. Twenty-four active but untrained men (23 ± 2 yr; VO2peak = 50 ± 6 mL · kg(-1) · min(-1)) ingested 3.2 g/day of β-ALA or a placebo (PLA) for a total of 10 weeks (n = 12 per group). Following 4 weeks of baseline supplementation, participants completed a 6-week SIT intervention. Each of 3 weekly sessions consisted of 4-6 Wingate tests, i.e., 30-s bouts of maximal cycling, interspersed with 4 min of recovery. Before and after the 6-week SIT program, participants completed a 250-kJ time trial and a repeated sprint test. Biopsies (v. lateralis) revealed that skeletal muscle carnosine content increased by 33% and 52%, respectively, after 4 and 10 weeks of β-ALA supplementation, but was unchanged in PLA. Total work performed during each training session was similar across treatments. SIT increased markers of mitochondrial content, including cytochome c oxidase (40%) and β-hydroxyacyl-CoA dehydrogenase maximal activities (19%), as well as VO2peak (9%), repeated-sprint capacity (5%), and 250-kJ time trial performance (13%), but there were no differences between treatments for any measure (p < .01, main effects for time; p > .05, interaction effects). The training stimulus may have overwhelmed any potential influence of β-ALA, or the supplementation protocol was insufficient to alter the variables to a detectable extent.
https://www.ncbi.nlm.nih.gov/pubmed/26008634

Med Sci Sports Exerc. 2006 Feb;38(2):334-8.
Carnosine and anserine ingestion enhances contribution of nonbicarbonate buffering.
Suzuki Y1, Nakao T, Maemura H, Sato M, Kamahara K, Morimatsu F, Takamatsu K.
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Abstract
PURPOSE:
The purpose of the present study was to investigate the effect of supplementation with chicken breast extract (CBEX), which was a rich source of carnosine and anserine, on acid-base balance and performance during intense intermittent exercise.
METHODS:
Eight male subjects performed intense intermittent exercise that consisted of 10 x 5-s maximal cycle ergometer sprints with a 25-s recovery period between each sprint. The subjects ingested 190 g of the test soup containing either CBEX or a placebo 30 min before the commencement of exercise. Arterial blood samples were collected at rest and during exercise to estimate the carnosine and anserine concentrations, pH, and bicarbonate concentration ([HCO3-]).
RESULTS:
Concentrations of anserine and its related amino acid significantly increased 30 min after CBEX supplementation, as compared with their values at rest. However, carnosine did not increase significantly. Following CBEX supplementation, the pH was significantly higher (P < 0.05) at the end of exercise, and [HCO3-] was also significantly higher (P < 0.05) during the latter half of exercise and after exercise. There were no significant differences in the total power and mean power of each set between the CBEX and placebo supplemented groups.
CONCLUSION:
Although oral supplementation with CBEX (which is a rich source of carnosine and anserine) increased the contribution of the nonbicarbonate buffering action and decreased bicarbonate buffering action in blood, intense intermittent exercise performance did not improve significantly.
https://www.ncbi.nlm.nih.gov/pubmed/16531904

Int J Sport Nutr. 1995 Dec;5(4):300-14.
Effects of multibuffer supplementation on acid-base balance and 2,3-diphosphoglycerate following repetitive anaerobic exercise.
Kraemer WJ1, Gordon SE, Lynch JM, Pop ME, Clark KL.
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Abstract
The purpose of this investigation was to determine the effects of a 3.5-day dietary multibuffer supplement (containing predominantly inorganic phosphate, or Pi, along with bicarbonate and carnosine, i.e., PhosFuel) on repetitive (four trials separated by 2 min rest) Wingate test (WT) performances and whole blood 2,3-diphosphoglycerate (2,3-DPG) concentrations in 10 recreationally trained road cyclists (T) and 10 normally active but untrained (UT) men. A 2-week washout period was utilized between experimental sessions. Venous blood samples were obtained via cannula once before exercise (baseline), immediately post each WT, and 3 min after the final WT (recovery). The data indicate that this supplement does not affect acid-base status with following intense anaerobic exercise and does not improve repetitive WT performance. However, the supplement does enhance post-exercise levels of 2,3-DPG and the 2,3-DPG/Hb ratio in recreationally trained cyclists while improving acute recovery of peak power in these men.
https://www.ncbi.nlm.nih.gov/pubmed/8605517